For a given frame $\{\zeta_i\}_{i=1}^\infty$, any Bessel sequence $\{\eta_i\}_{i=1}^\infty$ satisfying in the following identity for every $\xi\in H$ $$\xi=\sum_{i=1}^\infty \langle \xi, \eta_i\rangle \zeta_i$$ is called a dual frame associated with $\{\zeta_i\}_{i=1}^\infty$.

Q. What are the significant roles of the notion of dual frames in the progress of Frame theory. For example can we say that, if a frame is considered as a coded signal, any associated dual frame is used to decode it?!

Any other suggestion concerning its essential role?


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